Evaluate function using Cauchy's integral formula

Question

$$\int \frac{z^2 + z^7}{(z-e/3)^3} \, dz $$ where $\Gamma$ is a rectangular path traversed in the counterclockwise direction with vertices $1, 2i,−1,−2i.$ So I have noticed there is a singularity at $e/3.$ which also lies within the rectangle defined. I'm not sure what the next step is as substituting $e/3$ into the function gives an undefined value.

Answer 1

Let $f(z)=z^2+z^7$. Then, according to Cauchy's integral formula, your integral is equal to$$\frac{2!}{2\pi i}f''\left(\frac e3\right)=-\frac i\pi\times\left(2+\frac{14e^5}{81}\right).$$